The sum of the length and width of the rectangle is 14 cm, the length is 4 cm greater than the width.

The sum of the length and width of the rectangle is 14 cm, the length is 4 cm greater than the width. What is the area of this rectangle

The task
The length of the rectangle is a -? centimeters
Width of rectangle b -? centimeters
a + b = 14 centimeters
a – b = 4 centimeters
S -? square centimeters
Decision
1) Express the length of the rectangle a from one of the equations and substitute the value into the second equation
a + b = 14
a = 14 – b – substitute in a – b = 4
(14 – b) – b = 4
14 – 2 b = 4
2 b = 14 – 4 = 10
b = 10: 2
b = 5 (centimeters) – width
2) Calculate the length
a = 14 – b
a = 14 – 5
a = 9 (centimeters) – length
Checking a + b = 9 + 5 = 14, a-b = 9 – 5 = 4
3) Find the area of the rectangle
S = a b = 9 5 = 45 (square centimeters)
Answer: S = 45 cm ^ 2